--- In

primenumbers@yahoogroups.com, "leavemsg1" <leavemsg1@...>

wrote:

>

> --- In primenumbers@yahoogroups.com, "Bernhard Helmes" <bhelmes@>

> wrote:

> >

> > A beautifull evening,

> >

> > I try to give you a sufficent proof for primes p:=x^2+x+1

> >

> > p:=x^2+x+1=x*(x+1)+1 with p = 3 mod 4 => 2 appears only one time

as

> > divisor of p-1

> > p mod 3 = 1 or in other words 3 | p-1

> > p mod 9 > 1 => 3 appears only one time as divisor of p-1

> >

> > 2 ^ ((p-1)/2) = p-1 mod p, must be verified

> >

> > then p is prime

> >

>

> Hi, Bernhard.

> I think that x=15 is a counter-example... 2^((240/2)) == 1 mod 241.

> Is it? Bill

>

But p=241 is not congruent to 3 (mod 4). So it is not a counter-

example.

Best regards,

Dario Alpern

Buenos Aires - Argentina

http://www.alpertron.com.ar/ENGLISH.HTM